What is the derivative of 1/4 cos^4(x^3-sin^2(6x)) ?

The derivative of 1/4 cos^4(x^3-sin^2(6x)) is -3x^2cos^3(x^3)sin(x^3)-12sin(6x)cos(6x)

What is the first derivative of 1/4 cos^4(x^3-sin^2(6x)) ?

The first derivative of 1/4 cos^4(x^3-sin^2(6x)) is -3x^2cos^3(x^3)sin(x^3)-12sin(6x)cos(6x)

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\frac{d}{d x} (\frac{1}{4} cos^{4} (x^{3}) - sin^{2} (6 x))

- 3 x^{2} cos^{3} (x^{3}) sin (x^{3}) - 12 sin (6 x) cos (6 x)

Solution steps

\frac{d}{d x} (\frac{1}{4} cos^{4} (x^{3}) - sin^{2} (6 x))

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

= \frac{d}{d x} (\frac{1}{4} cos^{4} (x^{3})) - \frac{d}{d x} (sin^{2} (6 x))

\frac{d}{d x} (\frac{1}{4} cos^{4} (x^{3})) = - 3 x^{2} cos^{3} (x^{3}) sin (x^{3})

\frac{d}{d x} (sin^{2} (6 x)) = 12 sin (6 x) cos (6 x)

= - 3 x^{2} cos^{3} (x^{3}) sin (x^{3}) - 12 sin (6 x) cos (6 x)

What is the derivative of 1/4 cos^4(x^3-sin^2(6x)) ?
The derivative of 1/4 cos^4(x^3-sin^2(6x)) is -3x^2cos^3(x^3)sin(x^3)-12sin(6x)cos(6x)
What is the first derivative of 1/4 cos^4(x^3-sin^2(6x)) ?
The first derivative of 1/4 cos^4(x^3-sin^2(6x)) is -3x^2cos^3(x^3)sin(x^3)-12sin(6x)cos(6x)